A new approach to parallel computation of polynomial GCD and to related parallel computations over fields and integer rings

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn Part F129447, Issue , 1996, Pages 518-527

  Pan, Victor Y ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR SYSTEMS; POLYNOMIALS;

ARITHMETIC COMPLEXITY; LINEAR RECURRENCES; NEW APPROACHES; PARALLEL COMPUTATION; PARALLEL SOLUTIONS; STRUCTURED MATRIXES; TOEPLITZ LINEAR SYSTEMS; TOEPLITZ MATRICES;

MATRIX ALGEBRA;

EID: 33748369788     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. A.V. Aho, J.E. Hopcroft, J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Residing, Massachusetts, 1974.
2. R.R. Bitmead, B.D.O. Anderson, Asymptotically Fast Solution of Toeplitz and Related Systems of Linear Equations, Linear Algebra Appl., 34, 103-116, 1980.
3. R. P. Brent, F. G. Gustavson, D. Y. Y. Yun, Fast Solution of Toeplitz Systems of Equations and Computation of Padé Approximations, J. of Algorithms, 1, 259-295, 1980.
4. D. Bini, V.Y. Pan, Polynomial and Matrix Computations, Volume 1, Birkhauser, Boston, 1994.
5. D. G. Cantor, E. Kaltofen, On Fast Multiplication of Polynomials over Arbitrary Rings, Acta Inf., 28, 7, 697-701, 1991.
6. E. Kaltofen, V.Y. Pan, Processor Efficient Parallel Solution of Linear Systems over an Abstract Field, Proc. 3rd Ann. ACM Symp. on Parallel Algorithms and Architectures, 180-191, ACM Press, New York, 1991.
7. E. Kaltofen, V.Y. Pan, Processor Efficient Parallel Solution of Linear Systems II. The Positive Characteristic and Singular Cases, Proc. 33rd Ann. IEEE Symp. on Foundation of Computer Science, 714-723, IEEE Computer Society Press, 1992.
8. E. Kaltofen, V.Y. Pan, Parallel Solution of Toeplitz and Toeplitz-like Linear Systems over Fields of Small Positive Characteristic, Proc. First Intern. Symposium on Parallel Symbolic Computation (PASCO '94), Linz, (edited by Hoon Hong), Austria (Sept. 1994), Lecture Notes in Computing, 5, 225-233, World Scientific Publishing Company, Singapore, 1994.
9. R. Karp, V. Ramachandran, A Survey of Parallel Algorithms for Shared Memory Machines, Handbook for Theoretical Computer Science (J. van Leeuwen Editor), 869-941, North Holland, Amsterdam, 1990.
10. R.T. Moenck, J.H. Carter, Approximate Algorithms to Derive Exact Solutions to Systems of Linear Equations, Proc. EUROSAM, Lecture Notes in Computer Science, 72, 63-73, Springer, Berlin, 1979.
11. V.Y. Pan, Fast and Efficient Parallel Algorithms for the Exact Inversion of Integer Matrices, Proc. 5th Ann. Conference on Foundation of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, 206, 504-521, Springer, Berlin, 1985.
12. V.Y. Pan, Sequential and Parallel Complexity of Approximate Evaluation of Polynomial Zeros, Computer & Math. (with Applications), 14, 591-622, 1987.
13. V.Y. Pan, Computations with Dense Structured Matrices, Math. of Computations, 55, 191, 179-190, 1990.
14. V.Y. Pan, Parametrization of Newton's Iteration for Computations with Structured Matrices and Applications, Computers & Mathematics (with Applications), 24, 3, 61-75, 1992.
15. V.Y. Pan, Parallel Solution of Toeplitz-like Linear Systems, J. of Complexity, 8, 1-21, 1992.
16. V. Y. Pan, Decreasing the Displacement Rank of a Matrix, SIAM J. on Matrix Analysis, 14, 1, 118-121, 1993.
17. V.Y. Pan, Concurrent Iterative Algorithm for Toeplitz-like Linear Systems, IEEE Trans. on Parallel and Distributed Systems, 4, 5, 592-600, 1993.
18. V. Y. Pan, Effective Parallel Computations with Toeplitz and Toeplitz-like Matrices Filled with Integers, preprint, 1995.
19. V. Y. Pan, J. Reif, The Parallel Computation of the Minimum Cost Paths in Graphs by Stream Contraction, Information Processing Letters, 40, 79-83, 1991.
20. J. Reif, Work Efficient Parallel Solution of Toeplitz Systems and Polynomial GCD, Proc. 27th Ann. ACM Symp. on Theory of Computing, 751-761, ACM Press, NY, 1995.
21. A. Schönhage, The Fundamental Theorem of Algebra in Terms of Computational Complexity, manuscript, Dept. of Math., University of Tübingen, Tubingen, Germany, 1982.
22. A. Schönhage, Past Parallel Computation of Characteristic Polynomials by Leverrier's Power Sum Method Adapted to Fields of Finite Characteristic, Proc. 20th ICALP, Lecture Notes in Computer Science, 700, 410-417, Springer, Berlin, 1993.